Bandpass Filter Homework Statement

[Lucille]

Homework Statement

A simple way to build a bandpass filter is to filter the output of an RC highpass filter with an RC lowpass filter, as shown on the left in the diagram below. The isolation buffer is a circuit element that keeps the two circuits isolated so they behave as they would on their own. The (highly idealized) response of the circuit is shown on the right, where fL and fH are the low and high cutoff frequencies.

a) Assume fL is given by the equation for the cutoff frequency of a high pass filter, and fH is given by the equation for the cutoff frequency of a low pass filter. If the value of the resistors is 10 kOhm what should the value of the capacitors be if you were building an audio filter to allow vocal frequencies between fL = 80 Hz and fH = 1100Hz.

b) Assuming the high frequency behavior of the filter is described entirely by the response of the low pass filter, what would the gain, Vout/Vin, be at 10 000 Hz?

Image available at http://www.chegg.com/homework-help/questions-and-answers/simple-way-build-bandpass-filter-filter-output-rc-highpass-filter-rc-lowpass-filter-shown--q3608656

Homework Equations

f_c = 1/(RC*2Pi)

Vout/Vin = 1/ sqrt(1+(RwC)^2)

The Attempt at a Solution

a) C = 1/(2pi*f*R) -- do I calculate two different capacitance values?

so C1 = 1.99*10^-7 and C2 = 1.45*10^-8

b) Using C2 and plugging into the equation gives 0.568

 

[gneill]

Your capacitor values look fine.

I'm not sure about the formula you've used for the gain. What particular setup is it for? The question specifies that you consider only the low pass filter portion's contribution.

 

[Lucille]

It is for a low pass filter -- and so I used the value for C = 1.45 * 10^-8 F and subbed it into the equation for the gain of a low pass filter

 

[gneill]

It is for a low pass filter -- and so I used the value for C = 1.45 * 10^-8 F and subbed it into the equation for the gain of a low pass filter

Okay, that would be correct, but the result you've obtained looks a bit high to me. Can you check you math?

 

[Lucille]

Whoops - I got 0.109

 

[gneill]

Whoops - I got 0.109

Much better

 

[Lucille]

Thank you so so so much! It makes so much more sense to me now.